Sorry but I think when you watch the movie you get the feeling the freezing chamber IS in the main body of the city and not on the vane. When Luke gets sucked out the window he 'luckily' lands on the vane. The sudden reappearance of Vader whilst Luke was walking through the corridor of the vane makes you think shit how did he get there! Makes you jump! It just doesn't make sense that when Luke got separated from Artoo that he had such a long journey to face Vader (in a few seconds!!) or those seconds robbed.